Gigi, Inc. $($Gigi$),$ a U$.$S$.$ C$-$Corporation with a calendar year end, manufactures sporting goods at its plant in Forland, Georgia, as well as sources sporting goods manufactured by third$-$parties for resale. Gigi is known for its innovative and extensive research and experimental $($R&E$)$ activities, which are conducted in a separate facility in Ann Arbor, Michigan. As a result of these R&E activities, Gigi has a significant number of inventions that have been patented in the United States and other industrialized countries, including Japan. On January $1,2022,$ Gigi established a branch office in the United Kingdom $($UK$)$ to handle marketing, sales, and distribution of sporting goods sold throughout Europe. All the taxable income of the UK branch is foreign$-$source income. Prior to calendar year $2022,$ Gigi had no foreign$-$source income $($or loss$).$

Gigi$$s results for calendar year $2022$ were as follows:

$1.$ The UK branch office generated foreign$-$source income and UK taxable income of $$2,000,000,$ on which it paid UK income tax of $$400,000$ i$.$e$.,$ a flat UK income tax rate of $20$ percent.

$2.$ For U$.$S$.$ tax purposes, Gigi had deductible interest expense for the calendar year of $$3,000,000.$ Gigi$$s worldwide assets had an adjusted tax book basis of $$100,000,000,$ of which assets having an adjusted tax book basis of $$5,000,000$ generate the UK foreign$-$source income.

$3.$ For U$.$S$.$ tax purposes, in addition to the interest expense, Gigi allocated and apportioned $$30,000$ of deductible selling, general, and administrative $($SGA$)$ expenses and $$70,000$ of deductible R&E expenditures against its UK foreign$-$source income for foreign tax credit limitation purposes.

$4.$ Gigi had $$25,000,000$ of worldwide taxable income.

Assume a flat U$.$S$.$ corporate income tax rate of $21$ percent.

$($a$.)$ How much foreign income tax will Gigi be allowed to claim as a foreign tax credit on its $2022$ U$.$S$.$ corporate income tax return? At the end of calendar year $2022,$ describe Gigi$$s U$.$S$.$ foreign tax credit position $($excess credit or excess limitation$)$ and its significance.

$($b$.)$ In addition to the above facts, how would the following additional royalty income be sourced and would it change Gigi$$s U$.$S$.$ foreign tax credit position in $($a$.)$ if:

$(1)$ On January $1,2022,$ Gigi granted a non$-$exclusive license covering foreign patents on its sporting goods to an unrelated company organized under the laws of Japan, whereby the unrelated Japanese company was permitted to manufacture, sell, and distribute sporting goods in Japan; and

$(2)$ Gigi had received royalty income from the unrelated Japanese licensee of $$500,000,$ which were subject to a Japanese royalty withholding tax of ten percent $(10\%)$ i$.$e$.,$ $$50,000.$ For purposes of this question, assume that no deductible U$.$S$.-$based expenses $($e$.$g$.,$ interest, SGA, R&E$)$ would be allocated and apportioned against this royalty income.